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2D implementation of quantum annealing algorisms for fourth order binary optimization problems

Quantum annealing may provide advantages over simulated annealing on solving some problems such as Kth order binary optimization problem. No feasible architecture exists to implement the high-order optimization problem (K > 2) on current quantum annealing hardware. We propose a two-dimensional quantum annealing architecture to solve the 4th order binary optimization problem by encoding four-qubit interactions within the coupled local fields acting on a set of physical qubits. All possible four-body coupling terms for an N-qubit system can be implemented through this architecture and are readily realizable with the existing superconducting circuit technologies. The overhead of the physical qubits is O(N4), which is the same as previously proposed architectures in four-dimensional space. The equivalence between the optimization problem Hamiltonian and the executable Hamiltonian is ensured by a gauge invariant subspace of the experimental system. A scheme to realize local gauge constraint by single ancillary qubit is proposed.